Question

aflați numarul rațional x pentru fiecare dintre egalități​

Answer 1

Răspuns:

Explicație pas cu pas:

produsul mezilor este egal cu produsul extremilor

la primul am:

x^2=49

de unde rezulta x1=7

x2=-7

la al doilea

7*(x^2)=12*84

x^2=12*84/7

x^2=144

x1=12

x2=-12

si asa faci si la celelalte

Answer 2

$a)~\cfrac{x}{4,9} =\cfrac{10}{x} \Rightarrow x \cdot x=4,9 \cdot 10 \Rightarrow x^2=49\Rightarrow x=\pm\sqrt{49} \Rightarrow \boxed{x_1=-7}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\Rightarrow \boxed{x_2=7}\\\\b)~\cfrac{7x}{12} =\cfrac{84}{x} \Rightarrow 7x\cdot x=12 \cdot 84\Rightarrow 7x^2=1008 \Rightarrow x^2=\cfrac{1008}{7} \Rightarrow x^2=144\Rightarrow \\\\\Rightarrow x=\pm\sqrt{144} \Rightarrow \boxed{x_1=-12}\\\\~~~~~~~~~~~~~~~~~~~~\Rightarrow \boxed{x_2=12}$

$c)~\cfrac{2x}{125} =\cfrac{5}{8x} \Rightarrow 2x \cdot 8x=125 \cdot 5\Rightarrow 16x^2=625 \Rightarrow x^2=\cfrac{625}{16} \Rightarrow \\\\ \Rightarrow x=\pm\sqrt{\cfrac{625}{16} } \Rightarrow x=\pm \cfrac{\sqrt{625} }{\sqrt{16} } \Rightarrow \boxed{x_1=-\cfrac{25}{4} }\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\Rightarrow \boxed{x_2=\cfrac{25}{4} }$

$d)~\cfrac{x-2}{9} =\cfrac{25}{x-2} \Rightarrow (x-2)(x-2)=9 \cdot 25 \Rightarrow x^2-4x+4=225 \Rightarrow \\\\ \Rightarrow x^2-4x+4-225=0 \Rightarrow x^2-4x-221=0\\\\ \Delta=(-4)^2-4 \cdot 1 \cdot (-221)=16+884=900 > 0\\\\x_1=\cfrac{-(-4)-\sqrt{900} }{2 \cdot 1} \Rightarrow x_1=\cfrac{4-30}{2}\Rightarrow x_1= -\cfrac{26}{2} \Rightarrow \boxed{x_1=-13}\\\\x_2=\cfrac{-(-4)+\sqrt{900} }{2 \cdot 1}\Rightarrow x_2=\cfrac{4+30}{2} \Rightarrow x_2=\cfrac{34}{2} \Rightarrow \boxed{x_2=17}$

$e)~\cfrac{x-4}{-20}=\cfrac{5}{4-x} \Rightarrow(x-4)(4-x)=(-20)\cdot5\Rightarrow -x^2+8x-16=-100\Rightarrow\\\\\Rightarrow-x^2+8x-16+100=0\Rightarrow -x^2+8x+84=0 \Big|\cdot(-1)\Rightarrow\\\\\Rightarrow x^2-8x-84=0\\\\\Delta=(-8)^2-4\cdot1\cdot(-84)=64+336=400 > 0$

$x_1=\cfrac{-(-8)-\sqrt{400}}{2\cdot 1}\Rightarrow x_1=\cfrac{8-20}{2}\Rightarrow x_1=-\cfrac{12}{2}\Rightarrow \boxed{x_1=-6}\\\\x_2=\cfrac{-(-8)+\sqrt{400} }{2\cdot 1}\Rightarrow x_2=\cfrac{8+20}{2}\Rightarrow x_2=\cfrac{28}{2}\Rightarrow\boxed{x_2=14}$

$f)~\cfrac{\cfrac{1}{3}\cdot x }{8} =\cfrac{18}{12 \cdot x} \Rightarrow \cfrac{\cfrac{x}{3} }{8} =\cfrac{18}{12x}\Rightarrow \cfrac{x}{3} \cdot \cfrac{1}{8} =\cfrac{18}{12x} \Rightarrow \cfrac{x}{24} =\cfrac{18}{12x} \Rightarrow \\\\ \Rightarrow x \cdot 12x=24 \cdot 18 \Rightarrow 12x^2=432 \Rightarrow x^2=\cfrac{432}{12} \Rightarrow x^2=36 \Rightarrow \\\\ \Rightarrow x=\pm \sqrt{36} \Rightarrow \boxed{x_1=-6}\\\\~~~~~~~~~~~~~~~~~~\Rightarrow\boxed{x_2=6}$